This study investigates a standard vaccination game presuming the repeated-season framework, in which we mutually merge the dynamics of disease spread, which obeys the SIR process, and human decision-making as regards whether or not to get vaccinated at the beginning of each season with reference to the evolutionary game theory. We herein presume the Barabási–Albert scale-free (BA-SF) graph as an underlying network. Accordingly, we explore whether or not an additive noise to the transmission rate brings an advantageous stochastic resonance effect for confining a disease's spread. The results show that with a higher vaccination cost and/or a lower vaccine efficacy, the stochastic noise has no gap in vaccination coverage (VC) with the default without noise case, but brings a smaller final epidemic size (FES). In contrast, at a lower vaccination cost and a higher vaccine efficacy, the additive stochastic noise brings a smaller VC that consequently results in a larger FES than the default without noise case. This phenomenon is completely different from our previously reported bolstered enhancement effect of network reciprocity, in which each element of a payoff matrix is exposed to stochastic noise.